Basically, it is up to you how to customise your Fallout Boy. But some of the skills are more important than others. The age is almost of no importance as well as the gender, though a girl may have slight advantages because there are more male NPC's than females.

The traits have both advantages and disadvantages. The best ones are:

Gifted: higher base statistics; lower skill points, 5 skill points less per level. A fair trade-off, be sure to pick this one.

Small Frame: One point agility for less carryweight. Not bad, more primary statistics are always welcome. Until you get the powered Armour your NPCs can do the carrying for you.

Strength: 5 is enough; (The Enclave armour gives you +4; and the Red Memory Module gives you +1 for a total of 10)
Perception: 7 is enough and a Memory Module gives you the 8 points needed for the sniper perk (a real must have!)
Endurance: 6 is perfect (7 doesn't do you any good; HP formula: (1/2*EN + 2); 8 would be a waste of points needed otherwise)
Charisma: 7 is enough for the early stages of the game and another Module boosts you up to 8; this allows you to take 4 NPCs with you. If you really want 5 of them (and I know I do) take the Magnetic Personality Perk
Intelligence: 9 is really the minimum since this decides your skill points. (you might want to take 10 but there is a module for IN which would then go to waste)
 Skill points: (IN*2) + 5 -5 (gifted)
Agility: 9 is the minimum (since there is no module you need to take the Gain AG perk)
Luck: Not as useless as you might think; luck determines what kind of special random encounters you will find. And most importantly once you have the sniper (or for mêlée guys, the slayer) your chance for a critical hit is 10*Luck. I think you will end up 5 with because you need 7 to find good random encounters; (the Hubologist in NCR gives you +2)

So our hero has the following stats:

ST: 5, PE: 7, EN: 6, CH: 7, IN: 9, AG: 9, LK: 5

This allows you to solve most quests and get all the cool perks

Tag! Skills: Unarmed: Almost equal in damage to mêlée, but this one is necessary to do some quests. Especially the prize-fighter perk is very useful, but is only available to martial artists. Boost this to 130 until your reach San Francisco.
 Speech: Essential for a good guy, since most of the quests require you to be able to persuade people. You'll want to get this as high as 125 or so.
 Lockpick: Very important. There are lots of locks to pick for the chosen one. Steal is also quite useful, but you don't need to get this quite as high as lockpick (about 90)
 Science: Use every Big Book of Science you can find; You'll need to push this up to 125 in order to get the Brainbot (about the best NPC) and to hack certain computers.

There is a little trick when administering skill points around 100%. Set the difficulty to "hard" and your skills get lowered by 10%. Thus you can get to 110% with 10 instead of 20 points. Then for the actual task (like hacking the computer) you can switch to easy and get 20% on each skill.

Character development: Wait to level up unarmed until you trained with John Sullivan in Klammath.
 You may want to wait levelling up your small arms skill (up to maybe 100%) until after you find all of the G&B issues that are in the game before you reach Vault City. But after Vault City, you will need Small Arms.
 Also, Doctor is very useful. You can heal yourselves and your Companions with it. You can even restore cripples limbs. And, it gives you access to medical data in some computers. Without doctor you cannot learn about the combat implants in Vault City.
 You needn't raise barter, since you'll find lot's of stuff in the course of your adventure. If you ever need money, just run around on the map until you find some enemies.
 At level 12 or 15 pick the Tag! perk and either Energy Weapons or Big Guns, depending on your preference.

Status Upgrades

Strength:  +1 Memory Module (Vault 8 in Vault City)
   +4 Enclave Armour (Navarro)
Charisma:  +1 Memory Module (Navarro)
Perception:  +1 Memory Module (Military Base)
Intelligence: +1 Sierra Army Depot
Endurance:  +1 Vault 13
Luck:   +2 Hubologist in NCR
 

Perks

The best perks are: Awareness (lvl3)
Magnetic Personality (lvl6);
Explorer (lvl9);
Tag! (lvl12);
Bonus rate of fire (lvl 15)
Gain Agility (lvl 18)
Action Boy (*2) (lvl 21/27)
Sniper (lvl 24)

Maybe you prefer other perks, such as Healer or Pickpocket. Feel free to experiment which perk is best for your hero, the perks listed here are only a suggestion.

Gecko Skinning: After rescuing Smiley the Trapper from the Toxic Caves he returns to Buckner's Inn. Meet him there and he'll teach you some Outdoorsman tricks and the Gecko Skinning Perk. Now you can take the hides from slain Geckos with you. At the early stage of the game quite useful to make some money.
Prize-Fighter: Enter the Boxing Ring in New Reno (Jungle) and keep winning. After your last fight you'll be awarded the perk. Gives you 12 Damage Threshold against normal damage and 4% Damage Resistance against all kinds of attack.
Vault-City: Vault City has two perks to offer: Medical training gives you more % to doctor and first aid. You'll need doctor 60 to get this. Talk to Doctor Troy. He can also give you the second one: "Inoculations" (gives you poison and radiation resistance) But I'm not sure what the prerequisites for that are. Maybe you need to be poisoned or radiated...